Russian Roulette Puzzle

[clop]

Your friend is given two bullets and an unloaded six chamber revolver.

She loads the bullets in consecutive chambers and spins the drum.

She holds the gun to her head and pulls the trigger...



CLICK.


She grins and hands you the gun.

It's your turn to hold the gun to your head and pull the trigger.

The question is, if you want to live, should you spin the drum or not?

clop

[Ilya]

Yes you should.

This is a variation on Monty Haul Problem, made famous by Marilyn vos Savant. Without spinning the drum, your chances of decorating the opposite wall are 2/5, because one empty chamber is now out of running. With spinning the drum it is 1/3.

[Tog]

Your friend is given two bullets and an unloaded six chamber revolver.

She loads the bullets in consecutive chambers and spins the drum.

She holds the gun to her head and pulls the trigger...



CLICK.


She grins and hands you the gun.

It's your turn to hold the gun to your head and pull the trigger.

The question is, if you want to live, should you spin the drum or not?

clop

I take Walken's lead and play the Deer Hunter card.

Yes or no, depending on the make of the revolver. The newer giant caliber ones have a cylinder that is so smooth that if it's free to turn, the two loaded chambers will settle at the low point. If it's an older one, you can't rely on that.

Okay fine, I'll play. There are 6 possibilities before she pulls the trigger. 000011, 000110, 001100, 011000, 110000, and 100001. We know it can't be the last two or the gun would have gone off. She used up one of the other four options, leaving 3 possibilities, one of which will ruin your whole day. 66.6% chance of living.

If you spin the cylinder, the odds are two in six, so also a 66.6% chance of survival. I see it as even either way, so I'm sure I'm missing something.

[clop]

Keep trying.

clop

[Frog march]

well if he doesn't spin he has a one in three chance of dying.
if he does spin he has a one in six chance of dying.

so I say he should spin.

[Tog]

well if he doesn't spin he has a one in three chance of dying.
if he does spin he has a one in six chance of dying.

so I say he should spin.

Two bullets at the start though, so a 2 in 6, or 1 in 3 chance if he spins. Also, if the bullets are in consecutive chambers, her 'click' eliminates 3 of the possibilities. Both of the "hot" chambers, and one empty. We know that of the 5 remaining, only 1 combination will result in a bad day. The other bad one can't be accessed, so I guess the odds are 1 in 4, so I'd say don't spin.

[Sticks]

Can't you just chicken out ?

[brianok]

using the

000011, 000110, 001100, 011000, 110000, and 100001

example

the last 2 are eliminated

leaving 4 possibilities, only 1 of which is fatal. so you have a 75% chance of living by not spinning.

If you spin you only have a 66% chance of living.

So---------DON'T SPIN!!

[Tog]

So, Clop... Any answer for this?

[Eckelston]

Don't spin. The only way you're going to die if she got the one right before the first bullet. She couldn't he got the one before the second bullet else she wouldn't be grinning So, it's 1/4. If you spin it's 1/3. Oh, well others have got it earlier.

Now here's another question. You pull the trigger, click, you hand over the gun. Should she spin or not?

[SeanF]

Now here's another question. You pull the trigger, click, you hand over the gun. Should she spin or not?

My first reaction to this was, "Isn't that the same thing?" and then I realized you meant she gets the gun back after you've both "clicked."

In that case, it doesn't matter if she spins or not, it's 1 in 3 either way.

Now, if she clicks again and hands the gun back to you for your second try, you better spin...

[Eckelston]

My first reaction to this was, "Isn't that the same thing?" and then I realized you meant she gets the gun back after you've both "clicked."

In that case, it doesn't matter if she spins or not, it's 1 in 3 either way.

Now, if she clicks again and hands the gun back to you for your second try, you better spin...

Good try
But that's not the whole answer.

[SeanF]

Good try
But that's not the whole answer.

Hm. If she spins - and survives - you get to choose between 1 in 4 (not spinning) or 1 in 3 (spinning). However, if she doesn't spin - and survives - you have to choose between 1 in 2 (not spinning) or 1 in 3 (spinning).

That would mean while her odds of surviving this round are the same either way, her odds of having to take another round increase if she spins. It's better for her if she doesn't spin because that increases the odds you'll take a bullet on your next turn.

[perfessor]

When she "clicked", it meant that she landed on one of four safe chambers. BUT...If you are to click, she would have to have landed one one of THREE chambers - the first three, since the fourth brings a bullet into the next shot.

So: your odds without spinning are 3 in 6, or 50%. Better to spin again.

[hhEb09'1]

When she "clicked", it meant that she landed on one of four safe chambers. BUT...If you are to click, she would have to have landed one one of THREE chambers - the first three, since the fourth brings a bullet into the next shot.

So: your odds without spinning are 3 in 6, or 50%. Better to spin again.

Didn't you mean "3 in 4"? That would then agree with the other answers.

[swansont]

Yes or no, depending on the make of the revolver. The newer giant caliber ones have a cylinder that is so smooth that if it's free to turn, the two loaded chambers will settle at the low point. If it's an older one, you can't rely on that.

Though older revolvers tended to be large caliber, too, so there was plenty of weight. The truth is, there wasn't all that much bravado in playing with one round in the revolver.

The OP should have a statement about randomness in it.

[perfessor]

Didn't you mean "3 in 4"? That would then agree with the other answers.

Ah yes you are right and I was wrong. Her "click" narrows the sample space - your odds are 75% for surviving. Better NOT to spin.

Better yet, find a safer girlfriend.

[Tog]

Though older revolvers tended to be large caliber, too, so there was plenty of weight. The truth is, there wasn't all that much bravado in playing with one round in the revolver.

The OP should have a statement about randomness in it.

Yeah, but the cylinders on the new ones don't run on the stops like the older ones. We timed a 500 ruger (empty) and with one good flip it spun for just over 45 seconds. Different design now as opposed to decades ago. And no one commented on the Deer Hunter reference?

[Eckelston]

Hm. If she spins - and survives - you get to choose between 1 in 4 (not spinning) or 1 in 3 (spinning). However, if she doesn't spin - and survives - you have to choose between 1 in 2 (not spinning) or 1 in 3 (spinning).

That would mean while her odds of surviving this round are the same either way, her odds of having to take another round increase if she spins. It's better for her if she doesn't spin because that increases the odds you'll take a bullet on your next turn.

Yes, that's what I think too.

[Weird Dave]

Yes, that's what I think too.

I agree. I can post the numbers I calculated if people want.

Of course, the only sensible strategy for this game is to spin the drum exactly one space back every time your friend clicks. 100% survival beats 75% any day!